Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function

Salih Djilali; Soufiane Bentout; Tarik Mohammed Touaoula; Abdessamad Tridane; Sunil Kumar

doi:10.1016/j.rinp.2021.104953

Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function

Salih Djilali
, Soufiane Bentout
, Tarik Mohammed Touaoula
, Abdessamad Tridane
, Sunil Kumar

Abou Bakr Belkaïd University of Tlemcen
Benbouali Hassiba University of Chlef
Université d'ain Témouchent, Belhadj Bouchaib
United Arab Emirates University
National Institute of Technology Jamshedpur

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this research, we investigate the global properties of the heroin epidemic model with time distributed delay and nonlinear incidence function. We show that the system has threshold dynamics in terms of R₀, and we prove, a Lyapunov function, that for R₀<1 the drug-free equilibrium is globally asymptotically stable. For R₀>1, we give the persistence result of the heroin consumption. We also show the global stability of the endemic equilibrium for R₀>1 using a suitable Lyapunov function. The mathematical results are illustrated by numerically simulations.

Original language	English
Article number	104953
Journal	Results in Physics
Volume	31
DOIs	https://doi.org/10.1016/j.rinp.2021.104953
State	Published - Dec 2021
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Global stability
Lyapunov functional
Uniform persistence
Weak delay

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10.1016/j.rinp.2021.104953

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title = "Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function",

abstract = "In this research, we investigate the global properties of the heroin epidemic model with time distributed delay and nonlinear incidence function. We show that the system has threshold dynamics in terms of R0, and we prove, a Lyapunov function, that for R0<1 the drug-free equilibrium is globally asymptotically stable. For R0>1, we give the persistence result of the heroin consumption. We also show the global stability of the endemic equilibrium for R0>1 using a suitable Lyapunov function. The mathematical results are illustrated by numerically simulations.",

keywords = "Global stability, Lyapunov functional, Uniform persistence, Weak delay",

author = "Salih Djilali and Soufiane Bentout and Touaoula, \{Tarik Mohammed\} and Abdessamad Tridane and Sunil Kumar",

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doi = "10.1016/j.rinp.2021.104953",

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T1 - Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function

AU - Djilali, Salih

AU - Bentout, Soufiane

AU - Touaoula, Tarik Mohammed

AU - Tridane, Abdessamad

AU - Kumar, Sunil

PY - 2021/12

Y1 - 2021/12

N2 - In this research, we investigate the global properties of the heroin epidemic model with time distributed delay and nonlinear incidence function. We show that the system has threshold dynamics in terms of R0, and we prove, a Lyapunov function, that for R0<1 the drug-free equilibrium is globally asymptotically stable. For R0>1, we give the persistence result of the heroin consumption. We also show the global stability of the endemic equilibrium for R0>1 using a suitable Lyapunov function. The mathematical results are illustrated by numerically simulations.

AB - In this research, we investigate the global properties of the heroin epidemic model with time distributed delay and nonlinear incidence function. We show that the system has threshold dynamics in terms of R0, and we prove, a Lyapunov function, that for R0<1 the drug-free equilibrium is globally asymptotically stable. For R0>1, we give the persistence result of the heroin consumption. We also show the global stability of the endemic equilibrium for R0>1 using a suitable Lyapunov function. The mathematical results are illustrated by numerically simulations.

KW - Global stability

KW - Lyapunov functional

KW - Uniform persistence

KW - Weak delay

UR - https://www.scopus.com/pages/publications/85119051696

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DO - 10.1016/j.rinp.2021.104953

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VL - 31

JO - Results in Physics

JF - Results in Physics

M1 - 104953

ER -

Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function

Abstract

UN SDGs

Keywords

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